Theoretical Analysis of Engression and Reverse Markov Engression
arXiv:2606. 01002v1 Announce Type: cross Abstract: Engression is a recently proposed and effective framework for conditional distribution learning.
arXiv:2607. 27723v1 Announce Type: cross Abstract: Engression (Shen and Meinshausen, 2024) learns a conditional distribution by fitting a generative model $Y = f(X,\varepsilon)$ under the energy score, a strictly proper scoring rule.
arXiv:2606. 01002v1 Announce Type: cross Abstract: Engression is a recently proposed and effective framework for conditional distribution learning.
arXiv:2607. 18755v1 Announce Type: new Abstract: Flow-based models have established state-of-the-art performance in generative modeling across domains, but are hard to interpret due to their complex latent embeddings.
arXiv:2609.23789v1 Announce Type: new Abstract: Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SD...
Sufficiently Reduced Distributional Regression (SRDR) is a generative approach that merges conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). By framing SDR as a risk minimization problem using strictly proper scoring rules, SRDR jointly learns a dimension reduction map and a generative prediction model through minimization of the energy score, which can be estimated via sampling. The method extends to multi‑environment data and classification, and theoretical results show convergence of estimated conditional distributions in energy distance, implying asymptotic sufficiency. In experiments on CT slice localization, superconductivity data, and digit classification, SRDR recovers low‑dimensional sufficient structure and matches or surpasses state‑of‑the‑art nonlinear SDR methods in representation quality and predictive performance.
arXiv:2606. 23920v1 Announce Type: cross Abstract: The task of compositional generation involves using a conditional generative model, trained only on a subset of the possible conditions, to produce samples from compositionally-defined target distributions such as a geometric combination of the source distributions.
The paper presents a theoretical framework for approximating ratio-type functionals that arise in conditional generative modeling, specifically when the target density is expressed as a ratio of two kernel-based marginal densities. It proves that deep neural networks using the SignReLU activation can approximate these ratios with established L^p(Omega) bounds and convergence rates under standard regularity assumptions. Applying the framework to Denoising Diffusion Probabilistic Models, the authors construct a SignReLU-based estimator for the reverse process and derive bounds on the excess Kullback–Leibler risk, decomposing it into approximation and estimation errors to provide generalization guarantees for finite-sample training.
Flow-based models have established state-of-the-art performance in generative modeling across domains, but are hard to interpret due to their complex latent embeddings. In particular, the entanglement of generative factors in the latent space hinders controlled generation.
arXiv:2608. 11613v1 Announce Type: new Abstract: In this paper, we propose a local Sinkhorn divergence framework for conditional distribution reconstruction of multidimensional random fields.
arXiv:2509. 21925v2 Announce Type: replace-cross Abstract: This paper investigates the theoretical behavior of generative models under finite training populations.
BayesNDE is a neural density estimator that uses Bayesian generative modeling to estimate densities without relying on invertible networks or Jacobian-determinant calculations. It constructs an adaptive proposal for each observation by inferring a sample-specific latent posterior, and then applies bridge sampling to combine proposal samples with separate posterior samples for density estimation. Experiments on synthetic datasets show improved density estimation and structure recovery, while real-world applications demonstrate better anomaly detection.
arXiv:2607. 16725v1 Announce Type: cross Abstract: Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant.
arXiv:2608.22746v1 Announce Type: new Abstract: This paper studies the Sinkhorn distributionally robust hypothesis testing (SDRHT) problem, seeking a robust detector against least-favorable distribut...